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The martingale hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series

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Abstract

The main aim of this paper is to prove that for any 0 < p ≤ 2/3 there exists a martingale f ∈ H p such that Marcinkiewicz-Fejér means of the two-dimensional conjugate Walsh-Fourier series of the martingale f is not uniformly bounded in the space L p .

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References

  1. Marcinkiewicz, I.: Sur une methode remarquable de sommation des series doublefes de Fourier. Ann. Scuola Norm. Sup. Pisa, 8, 149–160 (1939)

    MATH  Google Scholar 

  2. Zhizhiashvili, L. V.: Generalizatin of a theorem of Marcinkiwicz (Russian). Izvest. AN USSR, Ser. Matem., 32, 1112–1122 (1968)

    Google Scholar 

  3. Weisz, F.: Convergence of double Walsh-Fourier series and Hardy spaces. Approx. Theory & Its. Appl. 17(2), 32–44 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Goginava, U.: The maximal operator of Marcinkiewicz-Fejér means of the d-dimensional Walsh-Fourier series. East J. Approx., 12(3), 295–302 (2006)

    MathSciNet  Google Scholar 

  5. Goginava, U.: The weak type inequality for the maximal operator of the Marcinkiewicz-Fejér means of the two-dimensional Walsh-Fourier series. J. Approximation Theory, 154(2), 161–180 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Weisz, F.: Martingale Hardy Spaces and Their Applications in Fourier Analysis, Springer, Berlin-Heidelberg-New York, 1994

    MATH  Google Scholar 

  7. Weisz, F.: Summability of Multi-dimensional Fourier Series and Hardy Space, Kluwer Academic, Dordrecht, 2002

    Google Scholar 

  8. Schipp, F., Wade, W. R., Simon, P., et al.: Walsh Series, An Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, New York, 1990

    MATH  Google Scholar 

  9. Golubov, B. I., Efimov, A. V., Skvortsov, V. A.: Series and Transformations of Walsh (Russian), Nauka, Moscow, 1987; English transl.: Kluwer Acad. Publ., 1991

    Google Scholar 

  10. Nagy, K.: Some convergence properties of the Walsh-Kaczmarz system with respect to the Marcinkiewicz means. Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl., 76, 503–516 (2005)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze str. 1, Tbilisi, 0128, Georgia

    Ushangi Goginava

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  1. Ushangi Goginava
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Correspondence to Ushangi Goginava.

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Goginava, U. The martingale hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series. Acta. Math. Sin.-English Ser. 27, 1949–1958 (2011). https://doi.org/10.1007/s10114-011-9551-7

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  • DOI: https://doi.org/10.1007/s10114-011-9551-7

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